Variational Learning of Euler–Lagrange Dynamics from Data - Ober-Blöbaum, Sina; Offen, Christian (Journal of Computational and Applied Mathematics)
The principle of least action is one of the most fundamental physical principle. It says that among all possible motions connecting two points in a phase space, the system will exhibit those motions which extremise an action functional. Many qualitative features of dynamical systems, such as the presence of conservation laws and energy balance equations, are related to the existence of an action functional. Incorporating variational structure into learning algorithms for dynamical systems is, therefore, crucial in order to make sure that the learned model shares important features with the exact physical system. In this paper we show how to incorporate variational principles into trajectory predictions of learned dynamical systems. The novelty of this work is that (1) our technique relies only on discrete position data of observed trajectories. Velocities or conjugate momenta do not need to be observed or approximated and no prior knowledge about the form of the variational principle is assumed. Instead, they are recovered using backward error analysis. (2) Moreover, our technique compensates discretisation errors when trajectories are computed from the learned system. This is important when moderate to large step-sizes are used and high accuracy is required. For this, we introduce and rigorously analyse the concept of inverse modified Lagrangians by developing an inverse version of variational backward error analysis. (3) Finally, we introduce a method to perform system identification from position observations only, based on variational backward error analysis.
Keywords: Lagrangian learning; variational backward error analysis; modified Lagrangian; variational integrators; physics informed learning

Backward error analysis for conjugate symplectic methods - McLachlan, Robert; Offen, Christian (Journal of Geometric Mechanics)
The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward error analysis. If the original and modified equation share structural properties, then the exact and approximate solution share geometric features such as the existence of conserved quantities. Conjugate symplectic methods preserve a modified symplectic form and a modified Hamiltonian when applied to a Hamiltonian system. We show how a blended version of variational and symplectic techniques can be used to compute modified symplectic and Hamiltonian structures. In contrast to other approaches, our backward error analysis method does not rely on an ansatz but computes the structures systematically, provided that a variational formulation of the method is known. The technique is illustrated on the example of symmetric linear multistep methods with matrix coefficients.
Keywords: variational integrators; backward error analysis; Euler--Lagrange equations; multistep methods; conjugate symplectic methods

Hamiltonian Neural Networks with Automatic Symmetry Detection - Dierkes, Eva; Offen, Christian; Ober-Blöbaum, Sina; Flaßkamp, Kathrin (Chaos)
Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when learning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite the data-driven modeling approach. However, preserving symmetries requires additional attention. In this research, we enhance the HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach allows to simultaneously learn the symmetry group action and the total energy of the system. As illustrating examples, a pendulum on a cart and a two-body problem from astrodynamics are considered.

Testinstrumente und Testdatenanalyse zur Verarbeitung von Unsicherheiten in Logikblöcken hochintegrierter Schaltungen - Sprenger, Alexander
Ever increasing demands on the performance of microchips are leading to ever more complex semiconductor technologies with ever shrinking feature sizes. Complex applications with high demands on safety and reliability, such as autonomous driving, are simultaneously driving the requirements for test and diagnosis of VLSI circuits. Throughout the life cycle of a microchip, uncertainties occur that affect its timing behavior. For example, weak circuit structures, aging effects, or process variations can lead to a change in the timing behavior of the circuit. While these uncertainties do not necessarily lead to a change of the functional behavior, they can lead to a reliability problem. With modular and hybrid compaction two test instruments are presented in this work that can be used for X-tolerant test response compaction in the built-in Faster-than-At-Speed Test (FAST) which is used to detect uncertainties in VLSI circuits. One challenge for test response compaction during FAST is the high and varying X-rate at the outputs of the circuit under test. By dividing the circuit outputs into test groups and separately compacting these test groups using stochastic compactors, the modular compaction is able to handle these high and varying X-rates. To deal with uncertainties on logic interconnects, a method for distinguishing crosstalk and process variation is presented. In current semiconductor technologies, the number of parasitic coupling capacitances between logic interconnects is growing. These coupling capacitances can lead to crosstalk, which causes increased current flow in the logic interconnects, which in turn can lead to increased electromigration. In the presented method, delay maps describing the timing behavior of the circuit outputs at different operating points are used to train artificial neural networks which classify the tested circuits into fault-free and faulty.
Keywords: Testantwortkompaktierung; Prozessvariation; Silicon Lifecycle Management

Explainable Integration of Knowledge Graphs Using Large Language Models - Ahmed, Abdullah Fathi Ahmed; Firmansyah, Asep Fajar; Sherif, Mohamed; Moussallem, Diego; Ngonga Ngomo, Axel-Cyrille (Natural Language Processing and Information Systems)
Linked knowledge graphs build the backbone of many data-driven applications such as search engines, conversational agents and e-commerce solutions. Declarative link discovery frameworks use complex link specifications to express the conditions under which a link between two resources can be deemed to exist. However, understanding such complex link specifications is a challenging task for non-expert users of link discovery frameworks. In this paper, we address this drawback by devising NMV-LS, a language model-based verbalization approach for translating complex link specifications into natural language. NMV-LS relies on the results of rule-based link specification verbalization to apply continuous training on T5, a large language model based on the Transformerarchitecture. We evaluated NMV-LS on English and German datasets using well-known machine translation metrics such as BLUE, METEOR, ChrF++ and TER. Our results suggest that our approach achieves a verbalization performance close to that of humans and outperforms state of the art approaches. Our source code and datasets are publicly available at https://github.com/dice-group/NMV-LS.

IngridKG: A FAIR Knowledge Graph of Graffiti - Sherif, Mohamed; Morim da Silva, Ana Alexandra; Pestryakova, Svetlana; Ahmed, Abdullah Fathi Ahmed; Niemann, Sven; Ngonga Ngomo, Axel-Cyrille
Graffiti is an urban phenomenon that is increasingly attracting the interest of the sciences. To the best of our knowledge, no suitable data corpora are available for systematic research until now. The Information System Graffiti in Germany project (Ingrid) closes this gap by dealing with graffiti image collections that have been made available to the project for public use. Within Ingrid, the graffiti images are collected, digitized and annotated. With this work, we aim to support the rapid access to a comprehensive data source on Ingrid targeted especially by researchers. In particular, we present IngridKG, an RDF knowledge graph of annotated graffiti, abides by the Linked Data and FAIR principles. We weekly update IngridKG by augmenting the new annotated graffiti to our knowledge graph. Our generation pipeline applies RDF data conversion, link discovery and data fusion approaches to the original data. The current version of IngridKG contains 460,640,154 triples and is linked to 3 other knowledge graphs by over 200,000 links. In our use case studies, we demonstrate the usefulness of our knowledge graph for different applications.

IndQNER: Named Entity Recognition Benchmark Dataset from the Indonesian Translation of the Quran - Gusmita, Ria Hari; Firmansyah, Asep Fajar; Moussallem, Diego; Ngonga Ngomo, Axel-Cyrille (Natural Language Processing and Information Systems)
Indonesian is classified as underrepresented in the Natural Language Processing (NLP) field, despite being the tenth most spoken language in the world with 198 million speakers. The paucity of datasets is recognized as the main reason for the slow advancements in NLP research for underrepresented languages. Significant attempts were made in 2020 to address this drawback for Indonesian. The Indonesian Natural Language Understanding (IndoNLU) benchmark was introduced alongside IndoBERT pre-trained language model. The second benchmark, Indonesian Language Evaluation Montage (IndoLEM), was presented in the same year. These benchmarks support several tasks, including Named Entity Recognition (NER). However, all NER datasets are in the public domain and do not contain domain-specific datasets. To alleviate this drawback, we introduce IndQNER, a manually annotated NER benchmark dataset in the religious domain that adheres to a meticulously designed annotation guideline. Since Indonesia has the world’s largest Muslim population, we build the dataset from the Indonesian translation of the Quran. The dataset includes 2475 named entities representing 18 different classes. To assess the annotation quality of IndQNER, we perform experiments with BiLSTM and CRF-based NER, as well as IndoBERT fine-tuning. The results reveal that the first model outperforms the second model achieving 0.98 F1 points. This outcome indicates that IndQNER may be an acceptable evaluation metric for Indonesian NER tasks in the aforementioned domain, widening the research’s domain range.

Partial observations, coarse graining and equivariance in Koopman operator theory for large-scale dynamical systems - Peitz, Sebastian; Harder, Hans; Nüske, Feliks; Philipp, Friedrich; Schaller, Manuel; Worthmann, Karl (arXiv:2307.15325)
The Koopman operator has become an essential tool for data-driven analysis, prediction and control of complex systems, the main reason being the enormous potential of identifying linear function space representations of nonlinear dynamics from measurements. Until now, the situation where for large-scale systems, we (i) only have access to partial observations (i.e., measurements, as is very common for experimental data) or (ii) deliberately perform coarse graining (for efficiency reasons) has not been treated to its full extent. In this paper, we address the pitfall associated with this situation, that the classical EDMD algorithm does not automatically provide a Koopman operator approximation for the underlying system if we do not carefully select the number of observables. Moreover, we show that symmetries in the system dynamics can be carried over to the Koopman operator, which allows us to massively increase the model efficiency. We also briefly draw a connection to domain decomposition techniques for partial differential equations and present numerical evidence using the Kuramoto--Sivashinsky equation.

Calibration of Large Coherent MIMO Radar Arrays: Channel Imbalances and 3D Antenna Positions - Greiff, Christian; Mateos-Núñez, David; Simoni, Renato; González-Huici, Maria; Kruse, Stephan; Scheytt, J. Christoph; Kolk, Karl; Höller, Christian; Kurz, Heiko Gustav; Meinecke, Marc-Michael; Gisder, Thomas (2023 24th International Radar Symposium (IRS))
One of the main challenges for next generation automotive radars is the improvement of angular resolution to a sub-degree level. In this context, wide aperture automotive radars of 1m length or more and resolution close to 0.1° in azimuth and 0.5° in elevation could be beneficial. To enable coherent processing of arrays with such large aperture, prior (i.e offline) and online calibration are necessary: channel imbalances (gains and phases) and three dimensional coordinates of transmit and receive elements need to be determined. We propose a calibration strategy based on alternating steps between the two subtasks of i) channel imbalance estimation with ‘known’ array positions, by applying a singular value decomposition to the resulting tensor calculus problem; and ii) antenna position estimation with ’known’ channel imbalances, by numerically maximizing the Bayesian posterior probability; in both cases operating on range/Doppler snapshots of disjoint targets (with potentially unknown locations). Simulation studies based on the parameters of a MIMO 8x6 linear sparse array show promising results as long as the initial position errors do not exceed half a wavelength (2mm), beyond which we observe strong effects of ambiguity. Experimental results with real measurements show that after calibration in laboratory conditions, our MIMO 8x6 demonstrator with 50cm aperture is able to resolve two targets at the same range with angular separation at least as close as 0.4°.

Finite-data error bounds for Koopman-based prediction and control - Nüske, Feliks; Peitz, Sebastian; Philipp, Friedrich; Schaller, Manuel; Worthmann, Karl (Journal of Nonlinear Science)
The Koopman operator has become an essential tool for data-driven approximation of dynamical (control) systems in recent years, e.g., via extended dynamic mode decomposition. Despite its popularity, convergence results and, in particular, error bounds are still quite scarce. In this paper, we derive probabilistic bounds for the approximation error and the prediction error depending on the number of training data points; for both ordinary and stochastic differential equations. Moreover, we extend our analysis to nonlinear control-affine systems using either ergodic trajectories or i.i.d. samples. Here, we exploit the linearity of the Koopman generator to obtain a bilinear system and, thus, circumvent the curse of dimensionality since we do not autonomize the system by augmenting the state by the control inputs. To the best of our knowledge, this is the first finite-data error analysis in the stochastic and/or control setting. Finally, we demonstrate the effectiveness of the proposed approach by comparing it with state-of-the-art techniques showing its superiority whenever state and control are coupled.

Multi-Objective Optimization for Sparse Deep Neural Network Training - Hotegni, Sedjro Salomon; Peitz, Sebastian; Berkemeier, Manuel Bastian (arXiv:2308.12243)
Different conflicting optimization criteria arise naturally in various Deep Learning scenarios. These can address different main tasks (i.e., in the setting of Multi-Task Learning), but also main and secondary tasks such as loss minimization versus sparsity. The usual approach is a simple weighting of the criteria, which formally only works in the convex setting. In this paper, we present a Multi-Objective Optimization algorithm using a modified Weighted Chebyshev scalarization for training Deep Neural Networks (DNNs) with respect to several tasks. By employing this scalarization technique, the algorithm can identify all optimal solutions of the original problem while reducing its complexity to a sequence of single-objective problems. The simplified problems are then solved using an Augmented Lagrangian method, enabling the use of popular optimization techniques such as Adam and Stochastic Gradient Descent, while efficaciously handling constraints. Our work aims to address the (economical and also ecological) sustainability issue of DNN models, with a particular focus on Deep Multi-Task models, which are typically designed with a very large number of weights to perform equally well on multiple tasks. Through experiments conducted on two Machine Learning datasets, we demonstrate the possibility of adaptively sparsifying the model during training without significantly impacting its performance, if we are willing to apply task-specific adaptations to the network weights. Code is available at https://github.com/salomonhotegni/MDMTN.

Efficient time stepping for numerical integration using reinforcement learning - Dellnitz, Michael; Hüllermeier, Eyke; Lücke, Marvin; Ober-Blöbaum, Sina; Offen, Christian; Peitz, Sebastian; Pfannschmidt, Karlson (SIAM Journal on Scientific Computing)
Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it results in prohibitively large errors or computational effort. To this end, adaptive schemes, such as solvers based on Runge–Kutta pairs, have been developed which adapt the step size based on local error estimations at each step. While the classical schemes apply very generally and are highly efficient on regular systems, they can behave suboptimally when an inefficient step rejection mechanism is triggered by structurally complex systems such as chaotic systems. To overcome these issues, we propose a method to tailor numerical schemes to the problem class at hand. This is achieved by combining simple, classical quadrature rules or ODE solvers with data-driven time-stepping controllers. Compared with learning solution operators to ODEs directly, it generalizes better to unseen initial data as our approach employs classical numerical schemes as base methods. At the same time it can make use of identified structures of a problem class and, therefore, outperforms state-of-the-art adaptive schemes. Several examples demonstrate superior efficiency. Source code is available at https://github.com/lueckem/quadrature-ML.

Low Power Streaming of Sensor Data Using Gray Code-Based Approximate Communication - Sadeghi-Kohan, Somayeh; Hellebrand, Sybille; Wunderlich, Hans-Joachim (2023 53rd Annual IEEE/IFIP International Conference on Dependable Systems and Networks Workshops (DSN-W))

Second grader´s understanding of doubling and halfing in various representations - Schwerin, Imke; Häsel-Weide, Uta (International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education)

Lehre in Zeiten von Digitalisierung und Inklusion - Beispiele aus drei Fächern - Schmidt, Rebekka; Tenberge, Claudia; Häsel-Weide, Uta (Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre)

Mit dem Leben Schritt halten - Eine Analyse des Wearable-Dispositivs - Schloots, Franziska Margarete
„Lerne deinen Körper besser kennen“, „Das Beste für deine Gesundheit“ und „Ihre Transformation beginnt jetzt“ - mit Versprechen wie diesen vermitteln die Produkttexte von Wearables wie Fitnesstracker und Smartwatches ein ganz bestimmtes Bild ihrer vorgesehenen Nutzer*innen und deren Nutzung. Verbunden mit den kleinen, am Handgelenk getragenen Geräten sind Fragen nach Erkenntnisgewinn und Kontrollverlust, Selbstoptimierung und Quantifizierungslogiken, Eigenverantwortung und Fremdsteuerung. Die vorliegende Arbeit widmet sich diesem komplexen Spannungsfeld und verfolgt dabei einen multiperspektivischen Ansatz: im Rahmen einer Dispositivanalyse werden die einzelnen Elemente des Wearable-Dispositivs als eigenständige, empirisch zu untersuchende Analysegegenstände betrachtet, um so das Zusammenwirken und die komplexe Beziehung von Diskursen, Gegenständen, Nutzung, Subjekten und Gesellschaft zu erforschen. Ein besonderes Erkenntnisinteresse liegt dabei auf dem Wissen, was sich über Wearables etabliert hat und sich in den Alltagspraktiken der Nutzer*innen widerspiegelt sowie bei der Frage nach den möglichen Funktionen und Auswirkungen des Wearable-Dispositivs.
Keywords: Selbstvermessung; Dispositivanalyse; Gesundheitsdiskurs; Quantifizierungsgesellschaft; Wearables; Selbstoptimierung

ElectricGrid.jl - A Julia-based modeling and simulationtool for power electronics-driven electric energy grids - Wallscheid, Oliver; Peitz, Sebastian; Stenner, Jan; Weber, Daniel; Boshoff, Septimus; Meyer, Marvin; Chidananda, Vikas; Schweins, Oliver (Journal of Open Source Software)
Keywords: General Earth and Planetary Sciences; General Environmental Science

Paradigmenwechsel vom klassischen zum datengetriebenen Problemlösen im Informatikunterricht - Höper, Lukas; Schulte, Carsten (MNU journal)

On the impossibility of surviving (iterated) deletion of weakly dominated strategies in rational MPC - Blömer, Johannes; Bobolz, Jan; Bröcher, Henrik

A Generic Construction of an Anonymous Reputation System and Instantiations from Lattices - Blömer, Johannes; Bobolz, Jan; Porzenheim, Laurens Alexander